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Hulls of cyclic serial codes over a finite chain ring. (English) Zbl 1476.14055

The Euclidean hull of a linear code over a finite field, introduced by E. F. Assmus jun. and J. D. Key in [Discrete Math. 83, No. 2–3, 161–187 (1990; Zbl 0707.51012)], is the intersection of the code and its Euclidean dual. Knowing the Euclidean hull or its dimension can be used to compute the automorphism group of the code or some of its parameters. S. Jitman et al. in [Discrete Math. 343, No. 1, Article ID 111621, 18 p. (2020; Zbl 1434.94098)] generalized the notion of Euclidean hull to cyclic codes over \({\mathbb Z}_4\) and obtained an algorithm to determine the type of the Euclidean hull of cyclic codes over \({\mathbb Z}_4\). Generalizing the methods of [Jitman et al., loc. cit.] the authors study the Euclidean hulls of a family of cyclic codes over finite chain rings and obtain an algorithm to compute the parameters of these Euclidean hulls. In particular, they characterize the Galois hulls of cyclic serial codes over finite chain rings, obtain the parameters of the Euclidean hull of cyclic serial codes, and compute the average dimension of the Euclidean hull of cyclic serial codes.

MSC:

14G50 Applications to coding theory and cryptography of arithmetic geometry
94B15 Cyclic codes
13B02 Extension theory of commutative rings
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References:

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